Rodrigues’ Rotation Formula is used to rotate a vector based on the Axis-Angle parameterization of attitude transformation. Given an axis and angle about which an initial vector is rotated, Rodrigues’ Formula yields the final orientation of the vector. However, Rodrigues’ Formula does not include the associated rotation about the vector axis, which depends on the specific trajectory used in slewing the axis from its initial to final orientation. A theorem in attitude kinematics that was not available when Rodrigues developed his formula, contains attitude components that should be included with Rodrigues’ Formula. These attitude components were previously applied to the related problem of the Foucault Pendulum, which rotates with the Earth about the Earth’s spin axis. The methods to compute the rotation angle about the vector axis are the same as those used to compute the rotation of the Foucault Pendulum’s mounting fixture, since the trajectories are similar. This work presents the derivation of the formula for the missing rotation angle of Rodrigues’s Formula. Several numerical examples are presented to illustrate the use of the formula.